Tagged Questions

Two graphs $G$ and $H$ are isomorphic if they have a function $f$ which provides an exact pairing of vertices in the two graphs such that for any adjacent vertices $u,v\in \{\mbox{set of vertices of }G\}$, $f(u)$ and $f(v)$ are also adjacent in $H$.

What is the easiest way to tell if these two graphs are isomorphic and how do I know which nodes in both graphs are the same. I've made the adjacency matrices but they are pretty big. I think I need ...

Take the complete graph $K_n$ ($n \geq 3$), on the red-colored vertex set $\mathbb{Z}_n$, say, and add a blue-colored $2$-path between each pair of vertices $v$, and $v+1$, we get a sequence of graphs ...

Let $k$ be a positive integer and let $T$ be a tree of order $k+3$. If $G$ is a graph with minimum degree at least $k+2$, prove that $G$ contains a subgraph isomorphic to $T$.
Any solutions or hints ...

I am having some trouble seeing why a graph of 4 nodes and 2 edges is not self-complementary such that G is isomorphic to G bar (G complement) (please see the attachment below). I know that the number ...